This year’s mathematics distinguished speaker, Moon Duchin from Tufts University, gave a talk on gerrymandering and the mathematics of voting rights Feb. 9 in the URBN Annex.
The talk was originally scheduled for Feb. 8 but was moved to the following day due to the Eagles victory parade.
Every seat in the screening room of URBN Annex was filled, and even the floor space was completely occupied by students, faculty and the general public before Duchin was set to speak at 3 p.m.
“This feels very strange to be a mathematician giving a talk to an overfull room,” Duchin joked as she came to the podium.
Duchin is an associate professor of math as well as the director of the Science, Technology and Society program at Tufts. She is also a fellow of the American Mathematical Society.
Duchin realized during her research at Tufts that her knowledge of metric geometry could span the realm of math into the field of politics, specifically gerrymandering, which is the redrawing of electoral districts to favor one political party over another. The party currently in charge of drawing district lines can weight votes in their favor to gain more seats.
This talk was particularly timely as the Pennsylvania Supreme Court ruled in January that the district lines drawn by the Republican-majority legislature were illegal. The governor of Pennsylvania, Tom Wolf, recently asked Duchin to help him in redrawing nonpartisan Congressional district maps.
To give context, Duchin began by discussing the history of gerrymandering in the United States, a word which dates back to post-revolutionary times in Massachusetts and has been happening across the country ever since.
A latere reason for redrawing district lines was racially motivated. In the South, lines were drawn to limit the rights of African-American voters. Duchin outlined the example of Tuskegee, Alabama, whose city lines were redrawn in 1957. That case made it to the Supreme Court in 1960.
“Tuskegee was almost 80 percent black and it became 100 percent white with the redrawn lines … what’s happening around this time is the stirrings of the civil rights movement and black people are registering to vote in greater numbers so that suddenly the 79 percent majority … [was] simply drawn out of the city,” Duchin said.
The Supreme Court found this case easy to handle, because it was blatant disenfranchisement and the drawing of these city lines was overturned.
Duchin explained that there are two main strategies in drawing district lines, packing and cracking. Packing is grouping together citizens that have the same interests and will most likely vote in the same way, such as keeping a district almost entirely Republicans or entirely Democrat. Cracking is the splitting up of voters so that one party can ensure that the opposite party cannot have a majority in that district. Both of these strategies tend to be used together, so that the party in control can gain more seats than they would have if lines were drawn differently.
Duchin made a point to note that gerrymandering happens all over the country and both parties are guilty of stacking the deck in their favor.
“Both parties gerrymander whenever they can, so let’s just get that out there. … Right now, we are seeing a lot of Republican gerrymanders because Republicans at the moment have 32 out of 50 legislatures, 33 out of 50 governors, and trifectas where they control both halves of the legislature plus the governorship in 27 out of 50 states … so there is a big disproportion right now in the ability to gerrymander,” Duchin said.
She also noted that sometimes gerrymandering can be friendly. A famous example of present day gerrymandering is seen in Chicago, with a map that is known as “The Earmuffs.” In this case, lines were drawn to connect two populations in a way that looks like a pair of earmuffs, with only a stretch of highway connecting them. The two populations were majority Puerto Rican and Mexican neighborhoods, and they were kept together so that their residents would get a representative that would keep their best interests in mind.
But other times, gerrymandering is not so friendly and seeks to exclude groups from having a voice. However, it is a difficult thing to draw maps that are completely neutral. There are many considerations when drawing district lines, such as the geography, population density, special interest voters, laws in place, etc.
Duchin believes that mathematics could help district lines to be drawn in a more bipartisan way. She commented that she doesn’t think that there will ever be a mathematical software that can draw a final district map for us, nor should there be, but she does think math could be used to determine how fair a current map is.
There are several things in place to measure how reasonable a district map is, such as compactness and contiguity. Compactness is how voter dense a district is based on the area, and contiguity is how the district is connected. There are several different ways to measure compactness using the perimeter and area of the district drawn. Contiguity can be seen through maps and what points they have connecting groups of people together.
“There’s an approach that’s percolating across the country called MCMC, or Markov Chain Monte Carlo. It is a random walk method that has been used with great success for 50 plus years, across domains in science, technology and engineering. It is the premier method for searching large spaces with unknown probability distributions,” Duchin explained.
This process can be used to search through maps and switch around boundaries thousands and millions of times. A program can be run with MCMC to explore many different possibilities of districts that can be made given a specific map and certain parameters. This analysis can be used to determine whether the districts that were actually drawn on a given map are in the realm of reasonability or if they are far too unlikely to have been drawn neutrally.
Duchin hopes that with the power of mathematics, blatant and unfair gerrymandering will be kept at bay in the future.
Duchin also gave another talk, directly after, which was more technical and addressed discrete curvature in redistricting and group theory.